A134388 A generalized Riordan array related to Hankel and Toeplitz+Hankel transforms.

1, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 6, 4, 2, 1, 6, 10, 8, 5, 2, 1, 10, 20, 15, 10, 6, 2, 1, 20, 35, 30, 21, 12, 7, 2, 1, 35, 70, 56, 42, 28, 14, 8, 2, 1, 70, 126, 112, 84, 56, 36, 16, 9, 2, 1, 126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1

Offset

0,5

Comments

Corresponds to the Riordan array ((1+2x)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108, with the first column replaced by 1,1,1,2,3,6,... with g.f. (1+2x+sqrt(1-4x^2))/(2*sqrt(1-4x^2)). Alternatively it is the array with first column 1,1,1,2,3,6,... and then the Riordan array ((1+2x)c(x)/sqrt(1-4x^2),xc(x^2)) embedded from the (1,1) position (indexing starting at (0,0)). Row sums are 2^n. Images of common sequences under this array have interesting Hankel transforms. For instance, the image of r^n has Hankel transform with g.f. 1/(1+(r^2-1)x^2).

Links

Table of n, a(n) for n=0..65.

E.L. Basor, T. Erhardt, Some identities for determinants of structured matrices, arXiv:math/0008075v1

Example

Triangle begins
1,
1, 1,
1, 2, 1,
2, 3, 2, 1,
3, 6, 4, 2, 1,
6, 10, 8, 5, 2, 1,
10, 20, 15, 10, 6, 2, 1,
20, 35, 30, 21, 12, 7, 2, 1,
35, 70, 56, 42, 28, 14, 8, 2, 1,
70, 126, 112, 84, 56, 36, 16, 9, 2, 1,
126, 252, 210, 168, 120, 72, 45, 18, 10, 2, 1

Crossrefs

Sequence in context: A133088 A059982 A187801 * A055095 A366770 A355249

Adjacent sequences: A134385 A134386 A134387 * A134389 A134390 A134391

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 23 2007

Status

approved